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EN
The log-rank test and Cox’s proportional hazard model can be used to compare survival curves but are limited by strict statistical assumptions. In this study, we introduce a novel, assumption-free method based on a random forest algorithm able to compare two or more survival curves. A proportion of the random forest’s trees with sufficient complexity is close to the test’s p-value estimate. The pruning of trees in the model modifies trees’ complexity and, thus, both the method’s robustness and statistical power. The discussed results are confirmed using a simulation study, varying the survival curves and the tree pruning level.
EN
Comparison of two time-event survival curves representing two groups of individuals' evolution in time is relatively usual in applied biostatistics. Although the log-rank test is the suggested tool how to face the above-mentioned problem, there is a rich statistical toolbox used to overcome some of the properties of the log-rank test. However, all of these methods are limited by relatively rigorous statistical assumptions. In this study, we introduce a new robust method for comparing two time-event survival curves. We briefly discuss selected issues of the robustness of the log-rank test and analyse a bit more some of the properties and mostly asymptotic time complexity of the proposed method. The new method models individual time-event survival curves in a discrete combinatorial way as orthogonal monotonic paths, which enables direct estimation of the p-value as it was originally defined. We also gently investigate how the surface of an area, bounded by two survival curves plotted onto a plane chart, is related to the test’s p-value. Finally, using simulated time-event data, we check the robustness of the introduced method in comparison with the log-rank test. Based on the theoretical analysis and simulations, the introduced method seems to be a promising and valid alternative to the log-rank test, particularly in case on how to compare two time-event curves regardless of any statistical assumptions.
3
Content available remote Predicting blood glucose using an LSTM neural network
EN
Diabetes self-management relies on the blood glucose prediction as it allows taking suitable actions to prevent low or high blood glucose level. In this paper, we propose a deep learning neural network model for blood glucose prediction. The model is a sequential one using a Long- Short-Term Memory (LSTM) layer with two fully connected layers. Several experiments were carried out over data of 10 diabetic patients to decide on the model's parameters in order to identify the best variant of the model. The performance of the proposed model measured in terms of root mean square error (RMSE) was compared with the ones of an existing LSTM model and an autoregressive (AR) model. The results show that our model is significantly more accurate; in fact, our LSTM model outperforms the existing LSTM model for all patients and outperforms the AR model in 9 over 10 patients, besides, the performance differences were assessed by thWilcoxon statistical test. Furthermore, the mean of the RMSE of our model was 12.38 mg/dl while it was 28.84 mg/dl and 50.69 mg/dl for AR and the existing LSTM respectively.
EN
The application of electronic elements introduces a number of advantages as well as disadvantages. The paper deals with advanced method of dependability - reliability analysis procedure of a highly reliable item. The data on manufacturing and operating of a few hundred thousands pieces of the highly reliable devices are available and from the statistical point of view they are very important collection/set. However, concerning some pieces of the items the manufacturing procedure of them was not made, controlled and checked accurately. The procedure described in the paper is based on the thorough data analysis aiming at the operation and manufacturing of these electronic elements. As the data sets collected are statistically non-coherent the objective of the paper is to make a statistical assessment and evaluation of the results. Failure rates calculations and their relation comparability regarding the both sets are presented in the paper.
5
Content available remote Zastosowanie rozkładu Suzuki w modelowaniu rzeczywistych zakłóceń biernych
PL
Artykuł prezentuje wyniki analizy zastosowania modelu Suzuki do opisu rzeczywistych zakłóceń biernych. Zaprezentowano postać oraz cechy modelu, warunki pomiaru rzeczywistych zakłóceń oraz metodę dopasowania parametrów modelu do badanych próbek. Analiza przeprowadzona we wnioskach pozwala określić możliwość opisu zakłóceń biernych za pomocą modelu Suzuki.
EN
Investigations of natural clutter characteristics have shown that such returns can be approximated by lognormal, Weibull or K distributions. Each of them approximates only some types of clutter. A Suzuki distribution, which produces the desired extended tail behaviour, has proved usefulness for modelling of radar clutter. The Suzuki model, which has a complicated integral form, has been accurately described. The samples of weather and ground clutter obtained from TRD-1222 RADAR (bandL) were analysed in order to approach the amplitude probability density function (apdf) to the Suzuki model. Two parameters of apdf were optimally approximated by using the ascending algorithm. The results of chi-square test have shown that Suzuki apdf can be satisfactorily used for modelling a weather clutter but not fully for ground clutter.
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